# Where does the graph of ln(x)-(ln(7-x))-9=y cross the x-axis?

The graph crosses the x-axis at $\left(6.999136 , 0\right)$

#### Explanation:

From the given equation:
$\ln \left(x\right) - \ln \left(7 - x\right) - 9 = y$

set $y = 0$ then solve for $x$

$\ln \left(x\right) - \ln \left(7 - x\right) - 9 = 0$
$\ln \left(\frac{x}{7 - x}\right) = 9$

$\left(\frac{x}{7 - x}\right) = {e}^{9}$

$x = {e}^{9} \cdot \left(7 - x\right)$

$x = 7 \cdot {e}^{9} - {e}^{9} \cdot x$

$\left(1 + {e}^{9}\right) x = 7 \cdot {e}^{9}$

$\frac{\cancel{\left(1 + {e}^{9}\right)} x}{\cancel{1 + {e}^{9}}} = \frac{7 \cdot {e}^{9}}{1 + {e}^{9}}$

$x = \frac{7 \cdot {e}^{9}}{1 + {e}^{9}}$

$x = 6.999136$

The graph crosses the x-axis at $\left(6.999136 , 0\right)$

Kindly check the graph ....

graph{y=ln x-ln(7-x)-9[-10,10,-20,20]}

Have a nice day !!! from the Philippines...